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Air Data System

The measurement of airspeed and altitude is fundamentally from a total (impact) pressure source and a static source located upon the aircraft. The following is a short attempt to describe the relations and methods for obtaining correct air data for flight test systems or production systems.

Airspeed Subsystem Calibration

Instrumentation

The instrumentation required on the test air vehicle for airspeed subsystem is as follows:

Boom Airspeed
Boom Altitude
Cone Altitude
Pilot's Airspeed
Pilot's Altitude
Pilot's Mach Number
Free Air Temperature (Ship's)
Free Air Temperature (Test)

In addition to these such basic parameters as gross weight, flap position, gear position, etc are necessary. For evaluation of "in ground effect"calibrations the ground speed and wind velocity are necessary.

Derivation of Theory - Pressure Lag Error

This subsection presents the theory of airspeed subsystem calibration including pressure lag error correction.

Flight tests to determine position errors of the airspeed subsystems installed in the air vehicle are performed at stabilized, level conditions where lag errors do not occur. This section describes the manner in which pressure lag corrections are applied to flight conditions where lag errors do occur.

An airspeed and altitude measuring system that contains a volume of air is subject to a pressure lag error when the air vehicle in which the system is installed changes air speed or altitude, as during a climb, descent or acceleration. Pressure lag is a result of:

a) Pressure drop in the system's tubing due to viscous friction.

b) Inertia of the air mass in the tubing.

c) Instrument friction.

d) The finite inertia and viscous and kinetic speed of pressure propagation (acoustic lag).

The following equation is derived, starting on page 28 of Reference 2:

where:

P = instantaneous pressure at the probe - in Hg

Pic = instantaneous pressure at the indicator - in Hg

dP/dt = rate of change of pressure - in Hg/sec

In the derivation of the above equation the following assumptions were made:

1) The rate of change of applied pressure is constant (dp/dt = K)

2) Laminar flow exists (Reynolds number is less than 2000)

3) The pressure lag is small compared to the applied pressure

4) The air and instrument inertias are negligible

5) The acoustic lag ( ) is negligible:

Where:
L = length of tubing - ft

C = speed of sound- ft/sec

6) The pressure drop across the orifices and restrictions is negligible.

7) is a constant. This is not strictly true as

= coefficient of absolute viscosity - lb-sec/ft2

P = pressure - in, Hg.

Since (assumption 7 above)

An emperical relation for ( 1/ 2) appears on page 67 of Reference 3:

Where T1 and T2 are temperatures at1 and 2 respectively - deg K

Therefore the equation used for pressure lag correction is:

Where:

= Pressure lag at Ta either static or total - sec
SL = Pressure lag at PaSL, TaSL (sea-level standard conditions) either static or total - sec

Ta = ambient temperature - deg K

Pic= Indicated pressure (either static or total)in. Hg.

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